Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric

A potent new mode of β-lactamase inhibition revealed by the 1.7 Å X-ray crystallographic structure of the TEM-1–BLIP complex

International audienceThe structure of TEM-1 beta-lactamase complex with the inhibitor BLIP has been determined at 1.7 angstrom resolution. The two tandemly repeated domains of BLIP form a polar, concave surface that docks onto a predominantly polar, convex protrusion on the enzyme. The ability of BLIP to adapt to a variety of class A beta-lactamases is most likely due to an observed flexibility between the two domains of the inhibitor and to an extensive layer of water molecules entrapped between the enzyme and inhibitor. A beta-hairpin loop from domain 1 of BLIP is inserted into the active site of the beta-lactamase. The carboxylate of Asp 49 forms hydrogen bonds to four conserved, catalytic residues in the beta-lactamase, thereby mimicking the position of the penicillin G carboxylate observed in the acyl-enzyme complex of TEM-1 with substrate. This beta-hairpin may serve as a template with which to create a new family of peptide-analogue beta-lactamase inhibitors

An evaluation of clients' needs and responsibilities in the construction process

The importance of clients' responsibilities in the construction process, as perceived by both clients and consultants, was assessed through a structured questionnaire survey. Using the relative index ranking technique, clients' fundamental needs and responsibilities in the construction process were analysed and ranked. Results indicate that the four most important needs are: functionality of the building, safety of the building, quality of the building, and completion time. The four most important clients' responsibilities identified by clients themselves are: planning/design, project finance, project implementation/management, and project definition/formulation. The four most important clients' responsibilities to project consultants are: project finance, project definition/formulation, planning/design, and project implementation/management. If both consultants and clients understand the fundamental needs of construction clients and if clients themselves are prepared to take an active role in the construction process, the chances of producing more successful projects will improve. © 1995 ©, MCB UP Limited. All rights reserved